Compactification of the group of rigid motions and applications to robotics
Nestor Djintelbe, Michel Coste (IRMAR)
TL;DR
This paper introduces a compactification of the 3D rigid motion group using the Study model and applies it to analyze robot configuration spaces and kinematic degenerations.
Contribution
It presents a novel compactification method for the rigid motion group and demonstrates its application in robot kinematics analysis.
Findings
Boundary analysis of robot configuration space
Degeneration of direct kinematics in certain parallel robots
Enhanced understanding of robot motion limits
Abstract
We introduce a compactification of the group of rigid motions in 3-space derived from the Study model for this group. We use this compactifi-cation in robot kinematics, by considering the boundary of the configuration space of a robot. We study in particular the degeneration of the direct kine-matic problem for some parallel robots with three degrees of freedom.
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Taxonomy
TopicsGeometric and Algebraic Topology · Robotic Mechanisms and Dynamics · Advanced Numerical Analysis Techniques